Schwartz $κ$-densities on the moduli stack of rank $2$ bundles near stable bundles
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909515949015040 |
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| author | Kazhdan, David Polishchuk, Alexander |
| author_facet | Kazhdan, David Polishchuk, Alexander |
| contents | Let $C$ be a curve over a non-archimedean local field of characteristic zero. We formulate algebro-geometric statements that imply boundedness of functions on the moduli space of stable bundles of rank $2$ and fixed odd degree determinant over $C$, coming from the Schwartz space of $κ$-densities on the corresponding stack of bundles (earlier we proved that these functions are locally constant on the locus of very stable bundles). We prove the relevant algebro-geometric statements for curves of genus $2$ and for non-hyperelliptic curves of genus $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schwartz $κ$-densities on the moduli stack of rank $2$ bundles near stable bundles Kazhdan, David Polishchuk, Alexander Algebraic Geometry Let $C$ be a curve over a non-archimedean local field of characteristic zero. We formulate algebro-geometric statements that imply boundedness of functions on the moduli space of stable bundles of rank $2$ and fixed odd degree determinant over $C$, coming from the Schwartz space of $κ$-densities on the corresponding stack of bundles (earlier we proved that these functions are locally constant on the locus of very stable bundles). We prove the relevant algebro-geometric statements for curves of genus $2$ and for non-hyperelliptic curves of genus $3$. |
| title | Schwartz $κ$-densities on the moduli stack of rank $2$ bundles near stable bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.10551 |